An option's arbitrage question

[ysun]

Hi everyone, recently I've been looking into some equity options scenarios, let's say currently NVDA price dropped after earnings, and we pull the option chain of it, given the same expiration date, if the strikes are evenly distributed and we have the call prices for each strike, how can I write some logic to detect if there is any simple arbitrage opportunity?

 

[lourano.x]

When I came across your question, I decided to model the scenario myself. Here's what I did:

I chose NVDA’s daily pricing data from the beginning of 2020 until March as a case study, which I believe aptly illustrates the pattern you’re referring to—a drop in price following earnings.

Moving to the modelling phase, I didn't do any complex SDEs and instead opted for a basic outline using polynomial regression, with volatility represented by the standard deviation of rolling returns. A sequence of strike prices was established at 5-point intervals. Lacking historical options pricing data, I used the binomial pricing model to estimate the call option prices for these predetermined strikes.

On the 40th day, corresponding to February 11th, which marked the early stages of an upswing, I decided to engage in a bull call spread with long strike 65 and short one 75. And here's a payoff distribution throw all simulations.

This is a simplified example, and I'm someone relatively new to the world of options, my simulation was quite rudimentary and I even didn't include transaction costs, correct interest rate and etc. But, I hope it provides a glimpse into the mechanics of such a scenario.

 

[ysun]

Thanks for your thoughts lourano, great charts and discussion.
My original thought was that there could be some potential theoretical constraints that bound the payoff range of all the vertical spreads and flies, also could expand to calendar spreads, such that when the realized volatility of the underlying asset spikes drastically, some market makers do not adjust their quotes accordingly and got picked off.